[Math Lair] Solutions for Practice Test 9, The Official SAT Study Guide, Section 8

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Here are solutions for section 8 of practice test #9 in The Official SAT Study Guide, second edition, found on pages 914–919. The solutions below demonstrate faster, more informal methods that might work better for you on a fast-paced test such as the SAT. To learn more about these methods, see my e-book Succeeding in SAT Math or the SAT math tips page.

  1. If 6,700 = 100(6k + 7), then 6,700 = 600k + 700, or 6,000 = 600k. So, k = 10. Select (C) 10.
  2. Since the dotted lines bisect the angles with measures x° and y°, then z = ½x + ½y = ½(70) + ½(40) = 55. Select (E) 55.
  3. Guess and check: Try each answer until you find one that does not fit:
  4. Guess and check: Starting with the smallest value, check to see whether it makes the equation true. For (A), |2 − 4| = 2, which is < 3. Select (A) 4. Note: If it turned out the smallest value didn't work, you should try the largest value next.
  5. If p is a factor of n + 3, then kp = n + 3, for some k. Now, n + 10 = n + 3 + 7 = kp + 7. Now, since p is a factor of n + 10, p is a factor of kp + 7. Since p is a factor of kp, then p must be a factor of 7 if p is a factor of kp + 7. If p is a factor of 7, then p = 1 or p = 7, since 7 is prime. We are told that p is greater than 1, so p = 7. Select (B) 7.
  6. When you see a problem like this, it's usually easiest to try to turn the expression that you have to evaluate into something resembling the givens. We can do that by factoring the expression:
      x²yxy²
    = xy(xy)
    = 7(5)
    = 35
    Select (D) 35.